If si di are metric spaces for i isin i where i is a, Ask an Expert

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If (Si , di ) are metric spaces for i ∈ I , where I is a finite set, then on the Cartesian product S = ITi ∈I Si let d(x, y) = },i di (xi , yi ).

(a) Show that d is a metric.

(b) Show that d metrizes the product of the di topologies.

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